International Recognition for Innovative Problem Solving

One student came up with a solution to one of the 5 problems on the Middle School version of the December contest that was better than the one devised by the problem writers at MOEMS.

The 4th through 8th graders at Rashi take the very well respected Mathematical Olympiads for Elementary and Middle School (MOEMS) competitions, an international competition.

Middle Schooler Jeremy G. came up with a solution to one of the 5 problems on the Middle School version of the December contest that was better than the one devised by the problem writers at MOEMS. Jeremy wrote up his solution to the problem and sent it to the proctors. They replied that they think it’s wonderful and they will be publishing it in their next newsletter. They have also written to every team telling them to credit Jeremy’s solution.

The Problem:

A palindrome reads the same forwards and backward. The number 2017102 is a 7-digit palindrome. Let A represent the least palindrome greater than 2017102. Let B represent the greatest palindrome less than 2017102. Find A-B.

Jeremy's letter follows:

Dear Math Olympiad [proctors],

While taking Division M Contest 2 dated December 13, 2017, I discovered an answer that is marked incorrect, but, according to the question, seems to be the correct answer.

The question [referenced above] is phrased in such a way that A and B are not constrained to be integers. My solution, which was not listed as correct, is the following:

Set A to 2017102.2017102 (the least real-number palindrome that is greater than 2017102).

Set B to 2017101.1017102 (the greatest real-number palindrome that is less than 2017202).

Subtracting B from A, you get 1.1, which is what I put down as my answer.

Originally, the organization intended the correct answer to be 2000, assuming that the palindromes chosen were integers. Nicholas Restivo, the Executive Director of MOEMS, was rightfully impressed by Jeremy's response. In an email back to his teacher, Cindy Carter, Nicholas writes, "Your Jeremy is a very bright person. He is absolutely correct... Please give him credit for that answer."